Sliding induced multiple polarization states in two-dimensional ferroelectrics

When the atomic layers in a non-centrosymmetric van der Waals structure slide against each other, the interfacial charge transfer results in a reversal of the structure’s spontaneous polarization. This phenomenon is known as sliding ferroelectricity and it is markedly different from conventional ferroelectric switching mechanisms relying on ion displacement. Here, we present layer dependence as a new dimension to control sliding ferroelectricity. By fabricating 3 R MoS2 of various thicknesses into dual-gate field-effect transistors, we obtain anomalous intermediate polarization states in multilayer (more than bilayer) 3 R MoS2. Using results from ab initio density functional theory calculations, we propose a generalized model to describe the ferroelectric switching process in multilayer 3 R MoS2 and to explain the formation of these intermediate polarization states. This work reveals the critical roles layer number and interlayer dipole coupling play in sliding ferroelectricity and presents a new strategy for the design of novel sliding ferroelectric devices.


Supplementary Figures and Tables
The crystal is ground to powder before XRD measurement.    (Fig. 1b), which is consistent with the schematic in Fig. 1a. The d-spacing of (110) plane is measured to be 1.5 Å. Since each layer in 3R phase is relatively shifted by a step of 1/3 unit cell in the direction of ( − ), each Mo atom is always aligned with two S atoms in c-axis direction (Fig. 1a). This atomic eclipse makes it impossible to differentiate the type of atoms using the STEM image contrast variations. The reverse is true in 2H
As shown in Fig. S10a, the FTJ is fabricated in a dual-gate setup with monolayer graphene as the top and bottom electrodes. Due to the limited density of states (DOS) in monolayer graphene, the electric field can penetrate the entire junction. The optical image of the device is shown in Fig. S10b. To investigate the switching process in the FTJ, the triangular waveform electric field illustrated in Fig. 3a is applied. In the on-field measurement, due to 17 the minimization of the carrier density variation in 3R MoS 2 by dual-gate regulation, the transport property of the FTJ is determined predominantly by the graphene layer and the 3R MoS 2 acts as an embedded dielectric layer.
As shown in Fig. S10c, a clear hysteresis caused by the ferroelectric switching of 3R MoS 2 can be observed. In each sweep direction, the curve is the combination of transport curves from the two graphene layers under the sweeping gate voltages. In the off-field measurement, the curve reflects the intrinsic property of the junction.
Because of the small reading voltage (1 mV) and the semimetal nature of graphene, the resistance of the junction mainly originates from the 3R MoS2. In compared to other paths, we investigate the origin of the energy barriers in all the paths. As shown in Fig. S17a and b, the energy profiles of the paths show close resemblance to their respective thickness profiles. It is noted that there is negligible change in the thickness of each S-Mo-S atomic layer during the ferroelectric switching process, hence all changes in thickness of the trilayer 3R MoS2 arise from changes in the vdW gap. This suggests that the energy barriers originate from electronic repulsion between the atomic layers. Furthermore, the size of vdW gap between two adjacent layers is independent from the movements or stacking orders of other layers, as shown in Fig. S17c. This suggests that the interlayer repulsion is short ranged and hence limited to the pair of layers that experiences the translation relative to each other. which involves the translation of the atomic layer with the S vacancy, shows a smaller energy barrier than the ABA-CBA process (see. Fig. S18) Hence the ABC-ABA process in this case is always energetically favourable compared to the ABC-CBC process. Similarly, the CBC-CBA process is always energetically favourable compared to the ABA-CBA process. Consequently, the ABC-ABA-CBA process is always preferred in the rampup process of this defect system, and the CBA-CBC-ABC process is always preferred in the ramp-down process.
In the actual experiment, where defects are inevitable, the switching process with the lower initial energy barrier is always preferred. This agrees well with our experimental observations where identical − ⊥ relationship is observed even after 40 cycles. The dashed horizontal line marks the height of energy barriers in the pristine case.
Despite the changes in the energy barriers, the difference in out-of-plane spontaneous polarizations between each corresponding polarization states of the two defect processes is negligible (see Fig. S19). This difference between the defective system and pristine system is also very small (see Fig. S19). As the 0.46% defect concentration is larger than what is usually present in experiment, the real-life change in spontaneous polarization in 3R MoS2 should not be significantly affected by S vacancy.